Continuous variable quantum secret sharing

1. A system for quantum secret sharing, the system comprising:

an optical link;

a trusted device;

a first device coupled with the trusted device through the optical link, the first device configured to

form a first quantum signal that carries a first random signal, and

launch the first quantum signal down the optical link to the trusted device;

one or more intermediary devices distributed along the optical link between the first device and the trusted device, each intermediary device configured to

form a respective quantum signal that carries an associated random signal, and

launch its quantum signal down the optical link to the trusted device coherently with the quantum signals launched down the optical link by the first device and the intermediary devices disposed upstream from the intermediary device;

wherein the trusted device is configured to

receive a coherent combination of the quantum signals from the upstream devices and detect a combined random signal indicative of the random signals carried on the received quantum signals,

for each upstream device, determine a respective key rate associated with the upstream device based on

a randomly selected portion of the random signal obtained from the upstream device via authenticated communication,

the corresponding portions of the random signals broadcast, by the respective remaining upstream devices, upon request by the trusted device, and

the corresponding portion of the combined random signal, and

produce, using reverse reconciliation from the remaining combined random signal, a secure key at a key rate equal to the minimum of the determined key rates, and

broadcast, to the upstream devices, decoding information to be used by the upstream devices to collaboratively determine the secure key, and a message encoded using the secure key.

2. The system of claim 1 , wherein the upstream devices are configured to collaborate with each other to

determine the secure key by using the broadcast decoding information and by sharing unpublished portions of the random signals, and

decode the broadcast message using the secure key.

3. The system of claim 1 , wherein each intermediary device comprises

a respective quantum-signal source configured to produce the associated quantum signal,

a respective combiner disposed in the optical link and configured to

transmit the quantum signals launched down the optical link by the first device and the intermediary devices disposed upstream from the intermediary device, and

receive, and redirect along the optical link, the locally produced quantum signal.

4. The system of claim 3 , wherein the combiner comprises an asymmetric beam splitter with a transmissivity in a range of 50-99%, and a reflectivity in a range of 50-1%.

5. The system of claim 3 , wherein each quantum-signal source comprises

a laser module configured to emit pulsed-laser light,

a signal generator configured to generate the respective random signal,

a modulator configured to modulate the pulsed-laser light in accordance with the random signal, and

an attenuator configured to reduce the power of the modulated pulsed-laser light to form the quantum signal.

6. The system of claim 5 , wherein the laser module comprises a solid-state laser with an emission spectrum in one of the O-band, the C-band, the L-band, the S-band, or the E-band.

7. The system of claim 5 , wherein the signal generator is configured to generate the random signal in accordance with a random-number distribution having a zero-mean Gaussian envelope.

8. The system of claim 3 , wherein

each upstream device further comprises a respective transducer, and

the quantum-signal source comprises

a thermal source configured to emit a random optical signal, and

a source beam splitter configured to transmit a fraction of the random optical signal as the quantum signal, and reflect the remaining random optical signal to the transducer,

wherein the transducer is configured to convert the reflected portion of the random optical signal to the random signal.

9. The system of claim 8 , wherein the thermal source comprises a super-luminescent diode.

10. The system of claim 8 , wherein the transducer comprises a homodyne detector.

11. The system of claim 3 , wherein the trusted device is configured to calibrate transmissions of the combiners by collaborating with the upstream devices.

12. The system of claim 1 , wherein the trusted device is configured to determine, for each upstream device, the respective key rate associated with the upstream device using security proof of two-party quantum-key distribution (QKD) between the upstream device and the trusted device.

13. The system of claim 1 , wherein the trusted device comprises a homodyne detector.

14. The system of claim 1 , wherein the trusted device is configured to, for each upstream device,

obtain, from the upstream device via authenticated communication, a randomly selected portion of the random signal,

access the corresponding portions of the random signals broadcast, upon request by the trusted device, by the respective remaining upstream devices, and

determine a respective key rate associated with the upstream device based on the corresponding portions of the random signals and of the combined random signal.

15. The system of claim 1 , wherein each intermediary device is configured to launch its quantum signal down the optical link in the same spatiotemporal mode as the quantum signals launched down the optical link by the first device and the intermediary devices disposed upstream from the intermediary device.

16. The system of claim 1 , wherein the optical link comprises one of a fiber optic or free space.

17. The system of claim 1 , wherein the one or more intermediary devices distributed along the optical link between the first device and the trusted device comprise up to one hundred intermediary devices.

18. A system for quantum secret sharing, the system comprising:

an optical link;

a trusted device;

a first device coupled with the trusted device through the optical link, the first device configured to:

form a first quantum signal that carries a first random signal, and

inject the first quantum signal into the optical link;

a second device disposed along the optical link between the first device and the trusted device, the second device configured to:

form a second quantum signal that carries a second random signal, and

inject the second quantum signal into the optical link coherently with the first quantum signal;

wherein the trusted device is configured to:

receive a coherent combination of the first and second quantum signals of the first and second devices,

detect a combined random signal indicative of the first and second random signals carried on the first and second quantum signals,

produce a secure key based, at least in part, on the combined random signal,

transmit, to the first and second devices, information to be used by the first and second devices to collaboratively determine the secure key;

wherein the trusted device, for each of the first and second devices, determines first and second key rates associated respectively with the first and second devices;

wherein the first key rate is based on 1) a first randomly selected portion of the first random signal obtained from the first device via authenticated communication, 2) a first key rate corresponding portion of the second random signal broadcast by the second device, and 3) a first key rate corresponding portion of the combined random signal; and

wherein the second key rate is based on 1) a second randomly selected portion of the second random signal obtained from the second device via authenticated communication, 2) a second key rate corresponding portions of the first random signal broadcast by the first device, and 3) a second key rate corresponding portion of the combined random signal.

19. The system of claim 18 wherein the trusted device is configured to produce, using reverse reconciliation from a portion of the combined random signal other than the first and second key rate corresponding portions, the secure key at a key rate equal to a minimum of the determined first and second key rates.

20. A system for quantum secret sharing, the system comprising:

an optical link;

a trusted device;

a first device coupled with the trusted device through the optical link, the first device configured to:

form a first quantum signal that carries a first random signal, and

inject the first quantum signal into the optical link;

a second device disposed along the optical link between the first device and the trusted device, the second device configured to:

form a second quantum signal that carries a second random signal, and

inject the second quantum signal into the optical link coherently with the first quantum signal;

wherein the trusted device is configured to:

receive a coherent combination of the first and second quantum signals of the first and second devices,

detect a combined random signal indicative of the first and second random signals carried on the first and second quantum signals,

produce a secure key based, at least in part, on the combined random signal, and

transmit, to the first and second devices, information to be used by the first and second devices to collaboratively determine the secure key; and

wherein the trusted device is configured to transmit, to the first and second devices, a message encoded using the secure key, and wherein the first and second devices are operable to decode the message using the collaboratively determined secure key.

21. The system of claim 20 wherein first and second devices are configured to determine the secure key by using the information transmitted from the trusted device and by sharing unpublished portions of the random signals.

22. The system of claim 20 wherein the optical link comprises one of a fiber optic or free space.

23. A system for quantum secret sharing, the system comprising:

an optical link;

a trusted device;

a first device coupled with the trusted device through the optical link, the first device configured to:

form a first quantum signal that carries a first random signal, and

inject the first quantum signal into the optical link;

a second device disposed along the optical link between the first device and the trusted device, the second device configured to:

form a second quantum signal that carries a second random signal, and

inject the second quantum signal into the optical link coherently with the first quantum signal;

wherein the trusted device is configured to:

receive a coherent combination of the first and second quantum signals of the first and second devices,

detect a combined random signal indicative of the first and second random signals carried on the first and second quantum signals,

produce a secure key based, at least in part, on the combined random signal,

transmit, to the first and second devices, information to be used by the first and second devices to collaboratively determine the secure key; and

wherein the second device includes a second device combiner optically coupled with the optical link, the second device is operable to obtain a phase reference of the first quantum signal, and use the second device combiner to coherently combine the second quantum signal with the first quantum signal that is incoming down the optical link to yield an outgoing coherent combination of first and second quantum signals based at least on the phase reference.

24. The system of claim 23 comprising a plurality of devices including the first and second devices, and wherein:

each of the plurality of devices is coupled with the trusted device through the optical link;

each of the plurality of devices is configured to:

form a respective quantum signal,

access a phase reference that is shared among the plurality of devices, and

inject, in accordance with the shared phase reference, the locally formed quantum signal into the optical link;

each of the respective quantum signals carries an associated random signal respectively provided by each of the plurality of devices;

the coherent combination received by the trusted device includes the respective quantum signal from each of the plurality of devices; and

the combined random signal is indicative of the associated random signal respectively provided by each of the plurality of devices.